Question #aec5e

Dec 11, 2016

$x = {e}^{e} - 1 \approx 14.154$

Explanation:

Using the property that ${e}^{\ln} \left(x\right) = x$, we have

$\ln \left(\ln \left(x + 1\right)\right) = 1$

$\implies {e}^{\ln \left(\ln \left(x + 1\right)\right)} = {e}^{1}$

$\implies \ln \left(x + 1\right) = e$

$\implies {e}^{\ln \left(x + 1\right)} = {e}^{e}$

$\implies x + 1 = {e}^{e}$

$\therefore x = {e}^{e} - 1 \approx 14.154$